Problem Statement:
Water in a canal, 6m wide and 1.5m deep, is flowing at a speed of 4 km/h. Determine how much area it will irrigate in 10 minutes if 10 cm of standing water is needed.

Solution:
To calculate the area irrigated by the flowing water, we need to determine the volume of water flowing in 10 minutes and then divide it by the standing water height.

Step 1: Calculate the Volume of Water Flowing:
The volume of water flowing per unit time can be calculated by multiplying the cross-sectional area of the canal by the velocity of water.

Given:
Width of the canal (w) = 6m
Depth of the canal (d) = 1.5m
Velocity of water (v) = 4 km/h

First, we need to convert the velocity from km/h to m/s:
1 km/h = 1000 m/3600 s = 5/18 m/s

So, the velocity of water (v) = 4 km/h = (4 * 5/18) m/s = 40/18 m/s

The cross-sectional area of the canal (A) = w * d = 6m * 1.5m = 9m²

Now, we can calculate the volume of water flowing in 10 minutes:
Volume of water (V) = A * v * t
where t is the time in seconds.

Given:
Time (t) = 10 minutes = 10 * 60 seconds = 600 seconds

Therefore,
Volume of water (V) = 9m² * (40/18)m/s * 600s

Step 2: Calculate the Area Irrigated:
To calculate the area irrigated, we need to divide the volume of water by the standing water height.

Given:
Standing water height (h) = 10cm = 0.1m

Area irrigated (A_irrigated) = V / h

Therefore,
Area irrigated (A_irrigated) = (9m² * (40/18)m/s * 600s) / 0.1m

Final Answer:
The water in the canal will irrigate an area of (9m² * (40/18)m/s * 600s) / 0.1m in 10 minutes, considering a standing water height of 10cm.